Solve the system x + y = 5 and 2x - y = 4.

Step 1: Write the system.

x + y = 5
2x - y = 4

Step 2: Add the equations.

Adding the left sides and right sides gives:

(x + y) + (2x - y) = 5 + 4

The y terms cancel:

3x = 9

Step 3: Solve for x.

Divide both sides by 3:

x = 3

Step 4: Substitute x = 3 into one of the original equations.

Use x + y = 5:

3 + y = 5

Step 5: Solve for y.

y = 2

Step 6: Check the solution in the second equation.

2(3) - 2 = 6 - 2 = 4

The equation is satisfied.

Therefore, the solution is (3, 2).